File size: 5,187 Bytes
e5a97c6 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 | import Mathlib
import OAI.Combinatorics.MatchingCount.Sampling.PM
import OAI.Combinatorics.MatchingCount.Graphs.Density
namespace OAI
namespace MatchingFPRAS.Transport
open Finset MatchingFPRAS.Replica
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler4BagEdgeFintype : Fintype (BagEdge bags) := Fintype.ofFinite _
variable (hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b)
variable (hG : G.IsAcyclic)
open Finset MatchingFPRAS.Replica
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler4BagEdgeFintype2 : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : L → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
include hheight hstep hD hw hbags hG
open Finset MatchingFPRAS.Replica
variable {V L : Type*} [Fintype V] [DecidableEq V] [Fintype L] [DecidableEq L]
variable {bags : V → Finset L} {G : SimpleGraph L}
noncomputable local instance finiteSampler4BagEdgeFintype3 : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : L → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℝ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
include hheight hstep hD hw hbags hG
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype4 : Fintype (BagEdge bags) := Fintype.ofFinite _
variable (hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b)
variable (hG : G.IsAcyclic)
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype5 : Fintype (BagEdge bags) := Fintype.ofFinite _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : J → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℕ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
include hheight hstep hD hw hbags hG
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype6 : Fintype (BagEdge bags) := Fintype.ofFinite _
noncomputable local instance finiteSampler4PMDecidableEq : DecidableEq (PM (BagEdge.Incident (bags := bags))) := Classical.decEq _
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype7 : Fintype (BagEdge bags) := Fintype.ofFinite _
noncomputable local instance finiteSampler4WeightedPMDecidableEq : DecidableEq (PM (BagEdge.Incident (bags := bags))) := Classical.decEq _
variable {hbags : ∀ v, ∀ a ∈ bags v, ∀ b ∈ bags v, a = b ∨ G.Adj a b}
variable {hG : G.IsAcyclic}
variable (height : J → ℝ) (hheight : ∀ l, 0 < height l)
variable (hstep : ∀ a b, G.Adj a b → height a ≤ 2 * height b)
variable (D : ℕ) (hD : 1 ≤ D) (w : BagEdge bags → ℝ)
variable (hw : ∀ e, height e.color / D ≤ w e ∧ w e ≤ 3 * height e.color)
include hheight hstep hD hw hbags hG
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype8 : Fintype (BagEdge bags) := Fintype.ofFinite _
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype9 : Fintype (BagEdge bags) := Fintype.ofFinite _
open Finset MatchingFPRAS.Replica
variable {V J : Type*} [Fintype V] [DecidableEq V] [Fintype J] [DecidableEq J]
variable {bags : V → Finset J} {G : SimpleGraph J}
noncomputable local instance finiteSampler4BagEdgeFintype10 : Fintype (BagEdge bags) := Fintype.ofFinite _
end MatchingFPRAS.Transport
end OAI
|